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dc.contributor.authorKalisch, Henrik
dc.contributor.authorMitrovic, Darko
dc.contributor.authorNordbotten, Jan Martin
dc.PublishedJournal of Mathematical Analysis and Applications 2015, 428(2):882-895eng
dc.description.abstractIt is shown how delta shock waves which consist of Dirac delta distributions and classical shocks can be used to construct non-monotone solutions of the Buckley–Leverett equation. These solutions are interpreted using a recent variational definition of delta shock waves in which the Rankine–Hugoniot deficit is explicitly accounted for [6]. The delta shock waves are also limits of approximate solutions constructed using a recent extension of the weak asymptotic method to complex-valued approximations [15]. Finally, it is shown how these non-standard shocks can be fitted together to construct similarity and traveling-wave solutions which are non-monotone, but still admissible in the sense that characteristics either enter or are parallel to the shock trajectories.en_US
dc.rightsAttribution CC BYeng
dc.subjectConservation lawseng
dc.subjectDelta shockseng
dc.subjectRiemann problemeng
dc.subjectWeak asymptoticseng
dc.subjectTraveling waveseng
dc.titleNon-standard shocks in the Buckley-Leverett equationen_US
dc.typePeer reviewed
dc.typeJournal article
dc.rights.holderCopyright 2015 The Authorsen_US
dc.relation.projectNorges forskningsråd: 215641
dc.subject.nsiVDP::Matematikk og naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414
dc.subject.nsiVDP::Mathematics and natural scienses: 400::Mathematics: 410::Algebra/algebraic analysis: 414

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